{"id":"https://openalex.org/W3105019514","doi":"https://doi.org/10.3390/computation6010022","title":"Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics","display_name":"Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics","publication_year":2018,"publication_date":"2018-02-26","ids":{"openalex":"https://openalex.org/W3105019514","doi":"https://doi.org/10.3390/computation6010022","mag":"3105019514"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation6010022","pdf_url":"https://www.mdpi.com/2079-3197/6/1/22/pdf?version=1519709370","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/6/1/22/pdf?version=1519709370","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021278553","display_name":"P\u00e9ter Koltai","orcid":"https://orcid.org/0000-0002-8127-6804"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"P\u00e9ter Koltai","raw_affiliation_strings":["Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060090190","display_name":"Hao Wu","orcid":"https://orcid.org/0000-0002-2170-0618"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hao Wu","raw_affiliation_strings":["Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055016850","display_name":"Frank No\u00e9","orcid":"https://orcid.org/0000-0003-4169-9324"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank No\u00e9","raw_affiliation_strings":["Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108704419","display_name":"Christof Sch\u00fctte","orcid":null},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christof Sch\u00fctte","raw_affiliation_strings":["Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","Zuse Institute Berlin, 14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Zuse Institute Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021278553"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515,"provenance":"doaj"},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515,"provenance":"doaj"},"fwci":2.48,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":37,"citation_normalized_percentile":{"value":0.999847,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"6","issue":"1","first_page":"22","last_page":"22"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9996,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9996,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9955,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9936,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-perfect-equilibrium","display_name":"Markov perfect equilibrium","score":0.46605667},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.43337083},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.41862565}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.53925645},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5189678},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5115593},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.49548686},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46883884},{"id":"https://openalex.org/C67091656","wikidata":"https://www.wikidata.org/wiki/Q6771328","display_name":"Markov perfect equilibrium","level":3,"score":0.46605667},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.43337083},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.4303192},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42382246},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.41862565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38766068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34724566},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.34529},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14855528},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11717966},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.093186736},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.084891826},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07534152},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation6010022","pdf_url":"https://www.mdpi.com/2079-3197/6/1/22/pdf?version=1519709370","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.04254","pdf_url":"http://arxiv.org/pdf/1801.04254","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://doaj.org/article/eee638cf60ed4cc69368784e66c5095e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.1801.04254","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation6010022","pdf_url":"https://www.mdpi.com/2079-3197/6/1/22/pdf?version=1519709370","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":["https://openalex.org/W2963224943","https://openalex.org/W3105019514"],"referenced_works_count":67,"referenced_works":["https://openalex.org/W1518747218","https://openalex.org/W1522256480","https://openalex.org/W1591018827","https://openalex.org/W1936027193","https://openalex.org/W1939606164","https://openalex.org/W1967640780","https://openalex.org/W1970442506","https://openalex.org/W1977875643","https://openalex.org/W1978450239","https://openalex.org/W1981145361","https://openalex.org/W1988220126","https://openalex.org/W1989544083","https://openalex.org/W1991901383","https://openalex.org/W1993622915","https://openalex.org/W2006690173","https://openalex.org/W2009447971","https://openalex.org/W2010766788","https://openalex.org/W2012029966","https://openalex.org/W2015656580","https://openalex.org/W2021820673","https://openalex.org/W2046290306","https://openalex.org/W2056211671","https://openalex.org/W2074388175","https://openalex.org/W2080076400","https://openalex.org/W2084417387","https://openalex.org/W2085213650","https://openalex.org/W2090500441","https://openalex.org/W2101116262","https://openalex.org/W2104049095","https://openalex.org/W2119640570","https://openalex.org/W2124138287","https://openalex.org/W2143592395","https://openalex.org/W2149801992","https://openalex.org/W2164193727","https://openalex.org/W2226825552","https://openalex.org/W2283941925","https://openalex.org/W2315297180","https://openalex.org/W2397367200","https://openalex.org/W2412945859","https://openalex.org/W2570547882","https://openalex.org/W2591704465","https://openalex.org/W2594932112","https://openalex.org/W2615252773","https://openalex.org/W2737465219","https://openalex.org/W2738080683","https://openalex.org/W2745805894","https://openalex.org/W2746954101","https://openalex.org/W2771020255","https://openalex.org/W2903866011","https://openalex.org/W2950662905","https://openalex.org/W2963115731","https://openalex.org/W2964129632","https://openalex.org/W3098063191","https://openalex.org/W3098891764","https://openalex.org/W3098898877","https://openalex.org/W3099205493","https://openalex.org/W3099674394","https://openalex.org/W3100184721","https://openalex.org/W3100810942","https://openalex.org/W3104046430","https://openalex.org/W3104914132","https://openalex.org/W3105904147","https://openalex.org/W3121991494","https://openalex.org/W4213311833","https://openalex.org/W585413800","https://openalex.org/W59181800","https://openalex.org/W649348608"],"related_works":["https://openalex.org/W4291951920","https://openalex.org/W2963262648","https://openalex.org/W2952827811","https://openalex.org/W2349674371","https://openalex.org/W2112835755","https://openalex.org/W2097495471","https://openalex.org/W2057862473","https://openalex.org/W2056202066","https://openalex.org/W1974173846","https://openalex.org/W1696545756"],"abstract_inverted_index":{"There":[0],"are":[1],"multiple":[2],"ways":[3],"in":[4,24,37],"which":[5],"a":[6,25,52],"stochastic":[7],"system":[8,53],"can":[9,85],"be":[10,17,23,36,51,86],"out":[11],"of":[12,65,74,92,96,116,122],"statistical":[13,72],"equilibrium.":[14],"It":[15],"might":[16,34,50],"subject":[18],"to":[19,44,55,104,119],"time-varying":[20],"forcing;":[21],"or":[22],"transient":[26],"phase":[27],"on":[28],"its":[29],"way":[30],"towards":[31],"equilibrium;":[32],"it":[33,48],"even":[35,49],"equilibrium":[38,58,75],"without":[39],"us":[40],"noticing":[41],"it,":[42],"due":[43],"insufficient":[45],"observations;":[46],"and":[47,76,80,113],"failing":[54],"admit":[56],"an":[57],"distribution":[59],"at":[60],"all.":[61],"We":[62,131],"review":[63],"some":[64],"the":[66,70,89,105,114,120],"approaches":[67],"that":[68,82],"model":[69],"effective":[71],"behavior":[73],"non-equilibrium":[77],"dynamical":[78],"systems,":[79],"show":[81],"both":[83],"cases":[84],"considered":[87],"under":[88],"unified":[90],"framework":[91],"optimal":[93],"low-rank":[94],"approximation":[95],"so-called":[97],"transfer":[98],"operators.":[99],"Particular":[100],"attention":[101],"is":[102],"given":[103],"connection":[106],"between":[107],"these":[108],"methods,":[109],"Markov":[110],"state":[111],"models,":[112],"concept":[115],"metastability,":[117],"further":[118],"estimation":[121],"such":[123],"reduced":[124],"order":[125],"models":[126],"from":[127],"finite":[128],"simulation":[129],"data.":[130],"illustrate":[132],"our":[133],"considerations":[134],"by":[135],"numerical":[136],"examples.":[137]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3105019514","counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-01-07T14:39:21.009737","created_date":"2020-11-23"}